Abstract

The topic of this paper is the study of Information Dissemination in Mobile Ad-hoc Networks by means of deterministic protocols. We characterize the connectivity resulting from the movement, from failures and from the fact that nodes may join the computation at different times with two values, α and β, so that, within α time slots, some node that has the information must be connected to some node without it for at least β time slots. The protocols studied are classiﬁed into three classes: oblivious (the transmission schedule of a node is only a
function of its ID), quasi-oblivious (the transmission schedule may also depend on a global time), and adaptive.
The main contribution of this work concerns negative results. Contrasting the lower and upper bounds derived, interesting complexity gaps among protocolclasses are observed. More precisely, in order to guarantee any progress towards solving the problem, it is shown that β must be at least n − 1 in general, but
that β ∈ Ω(n 2/ log n) if an oblivious protocol is used. Since quasi-oblivious protocols can guarantee progress with β ∈ O(n), this represents a signiﬁcant gap,
almost linear in β, between oblivious and quasi-oblivious protocols. Regardingthe time to complete the dissemination, a lower bound of Ω(nα + n 3/ log n) is proved for oblivious protocols, which is tight up to a polylogarithmic factor
because a constructive O(nα + n 3 log n) upper bound exists for the same class. It is also proved that adaptive protocols require Ω(nα + n 2), which is optimal given that a matching upper bound can be proved for quasi-oblivious protocols. These results show that the gap in time complexity between oblivious and quasioblivious, and hence adaptive, protocols is almost linear. This gap is what we call the proﬁt of global synchrony, since it represents the gain the network obtains from global synchrony with respect to not having it.